Various proposals have been made heretofore for constructing a building (either a single-story building or a multistory building) with precast concrete wall panels. One such proposal is disclosed in U.S. Pat. No. 2,592,634 to J. H. Wilson. For various reasons these previous proposals have not received substantial acceptance, principally because of the complexity and cost of constructing such buildings despite the ostensible advantages of their prefabricated modular designs.